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Generalized Large deviation principles was developed for Colombeau-Ito SDE with a random coefficients. We is significantly expand the classical theory of large deviations for randomly perturbed dynamical systems developed by Freidlin and Wentzell.Using SLDP approach, jumps phenomena, in financial markets, also is considered. Jumps phenomena, in financial markets is explained from the first principles, without any reference to Poisson jump process. In contrast with a phenomenological approach we explain such jumps phenomena from the first principles, without any reference to Poisson jump process.
The Large Deviations Principle (LDP) is verified for a homogeneous diffusion process with respect to a Brownian motion $B_t$, $$ X^eps_t=x_0+int_0^tb(X^eps_s)ds+ epsint_0^tsigma(X^eps_s)dB_s, $$ where $b(x)$ and $sigma(x)$ are are locally Lipschitz f
The superstable Weakly Imperfect Bose Gas {(WIBG)} was originally derived to solve the inconsistency of the Bogoliubov theory of superfluidity. Its grand-canonical thermodynamics was recently solved but not at {point of} the {(first order)} phase tra
We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth-death process on a lattice, with rates derived from Kramers law as an approximation of
In this paper we extend the results of Lenci and Rey-Bellet on the large deviation upper bound of the distribution measures of local Hamiltonians with respect to a Gibbs state, in the setting of translation-invariant finite-range interactions. We sho
The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallographic finite reflection groups $H_2$, $H_3$ and $H_4$. Using a represent